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  4. A material particle with a rest mass m0 is moving with speed of light c. The de-Broglie wavelength associated is given by

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Q. A material particle with a rest mass $m_0$ is moving with speed of light c. The de-Broglie wavelength associated is given by

Dual Nature of Radiation and Matter

Solution:

$ \lambda = \frac{ h }{ mv} $ where, m = $ \frac{ m_0 }{ \sqrt{ 1 - \frac{ v^2 }{ c^2 } }} $
As v = c, then
$ \Rightarrow m = \frac{ m_0 }{ \sqrt{ 1 - \frac{ c^2 }{ c^2 } }} = \frac{ m_0 }{ \sqrt{ 1 - 1}} = \frac{ m_0 }{ 0 } $
$ \Rightarrow m = \infty $,
Hence, $ \, \lambda = \frac{ h }{ \infty} = 0 $